Finite-size Effects on The Edge Loss Probability in Non-Hermitian Quantum Walks

TL;DR

This paper investigates how finite-size effects influence the edge loss probability in non-Hermitian quantum walks, revealing that boundary scattering can suppress or enhance edge loss depending on the system parameters.

Contribution

It demonstrates the impact of finite-size boundary scattering on edge loss probability, extending the understanding of non-Hermitian quantum walks beyond the infinite limit.

Findings

Boundary scattering can suppress edge loss in finite chains.

Imaginary gap opening can induce large edge loss.

Finite-size effects significantly alter edge dynamics.

Abstract

A dynamical bulk-edge relation in quantum walks has been theoretically proposed and experimentally observed, in which a power-law dependence of the bulk loss probability is associated with a pronounced peak of loss probability at the edge. This behavior has been proven to arise from imaginary gap closing and the non-Hermitian skin effect in the infinite limit without boundary effects. However, in a finite-size chain, we find that boundary scattering can suppress this edge burst. Meanwhile, imaginary gap opening together with the non-Hermitian skin effect, can also induce a large loss probability at the edge. Our results provide insights into finite-size quantum dynamics.